Choose the correct alternative:If ⌊.⌋ denotes the greatest integer less than or equal to the real number under consideration and – 1 ≤ x < 0, 0 ≤ y < 1, 1 ≤ z ≤ 2, then the value - Mathematics

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Choose the correct alternative:
If ⌊.⌋ denotes the greatest integer less than or equal to the real number under consideration and – 1 ≤ x < 0, 0 ≤ y < 1, 1 ≤ z ≤ 2, then the value of the determinant $[\begin{matrix} [x] + 1 & [y] & [z] \\ [x] & [y] + 1 & [z] \\ [x] & [y] & [z] + 1 \end{matrix}]$

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[z]
[y]
[x]
[x] + 1

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[z]

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Determinants

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

Q 19 Q 18 Q 20

पाठ 7: Matrices and Determinants - Exercise 7.5 [पृष्ठ ४२]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board

पाठ 7 Matrices and Determinants
Exercise 7.5 | Q 19 | पृष्ठ ४२

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Show that $| \begin{matrix} b + c & bc & b^{2} C^{2} \\ c + a & ca & c^{2} a^{2} \\ a + b & ab & a^{2} b^{2} \end{matrix} |$ = 0

Prove that $| \begin{matrix} a^{2} & bc & ac + c^{2} \\ a^{2} + ab & b^{2} & ac \\ ab & b^{2} + bc & c^{2} \end{matrix} | = 4 a^{2} b^{2} c^{2}$

Prove that $| \begin{matrix} 1 + a & 1 & 1 \\ 1 & 1 + b & 1 \\ 1 & 1 & 1 + c \end{matrix} | = abc (1 + \frac{1}{a} + \frac{1}{b} + \frac{1}{c})$

If A = $[\begin{matrix} \frac{1}{2} & α \\ 0 & \frac{1}{2} \end{matrix}]$ , prove that $\sum_{k = 1}^{n} \det (A^{k}) = \frac{1}{3} (1 - \frac{1}{4})$

If A and B are square matrices of order 3 such that |A| = –1 and |B| = 3, find the value of |3AB|

Determine the roots of the equation $| \begin{matrix} 1 & 4 & 20 \\ 1 & - 2 & 5 \\ 1 & 2 x & 5 x^{2} \end{matrix} |$ = 0

Show that $| \begin{matrix} 1 & 1 & 1 \\ x & y & z \\ x^{2} & y^{2} & z^{2} \end{matrix} |$ = (x – y)(y – z)(z – x)

Find the area of the triangle whose vertices are (0, 0), (1, 2) and (4, 3)

Identify the singular and non-singular matrices:

$[\begin{matrix} 0 & a - b & k \\ b - a & 0 & 5 \\ - k & - 5 & 0 \end{matrix}]$

Determine the values of a and b so that the following matrices are singular:

A = $[\begin{matrix} 7 & 3 \\ - 2 & a \end{matrix}]$

Choose the correct alternative:
if Δ = $| \begin{matrix} a & b & c \\ x & y & z \\ p & q & r \end{matrix} |$ then $| \begin{matrix} ka & kb & kc \\ k x & k y & k z \\ kp & kq & kr \end{matrix} |$ is

Choose the correct alternative:
If x₁, x₂, x₃ as well as y₁, y₂, y₃ are in geometric progression with the same common ratio, then the points (x₁, y₁), (x₂, y₂), (x₃, y₃) are

Choose the correct alternative:
If A = $| \begin{matrix} - 1 & 2 & 4 \\ 3 & 1 & 0 \\ - 2 & 4 & 2 \end{matrix} |$ and B = $| \begin{matrix} - 2 & 4 & 2 \\ 6 & 2 & 0 \\ - 2 & 4 & 8 \end{matrix} |$ , then B is given by

Find the area of the triangle with vertices at the point given is (1, 0), (6, 0), (4, 3).

Let a, b, c, d be in arithmetic progression with common difference λ. If $| \begin{matrix} x + a - c & x + b & x + a \\ x - 1 & x + c & x + b \\ x - b + d & x + d & x + c \end{matrix} |$ = 2, then value of λ² is equal to ______.

If $| \begin{matrix} 1 + x & x & x^{2} \\ x & 1 + x & x^{2} \\ x^{2} & x & 1 + x \end{matrix} |$ = ax⁵ + bx⁴ + cx³ + dx² + λx + µ be an identity in x, where a, b, c, d, λ, µ are independent of x. Then the value of λ is ______.

If $x \in R | \begin{matrix} 8 & 2 & x \\ 2 & x & 8 \\ x & 8 & 2 \end{matrix} |$ = 0, then $| \frac{x}{2} |$ is equal to ______.

Let S = ${(\begin{matrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{matrix}) : a_{i j} \in {0, 1, 2}, a_{11} = a_{22}}$

Then the number of non-singular matrices in the set S is ______.

Choose the correct alternative:If ⌊.⌋ denotes the greatest integer less than or equal to the real number under consideration and – 1 ≤ x < 0, 0 ≤ y < 1, 1 ≤ z ≤ 2, then the value - Mathematics

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Choose the correct alternative:If ⌊.⌋ denotes the greatest integer less than or equal to the real number under consideration and – 1 ≤ x < 0, 0 ≤ y < 1, 1 ≤ z ≤ 2, then the value - Mathematics

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